Department of Technical and Engineering, Science & Research Branch, Islamic Azad University, Tehran, Iran.
ISA Trans. 2011 Jan;50(1):21-7. doi: 10.1016/j.isatra.2010.10.007. Epub 2010 Nov 18.
In this paper, the stabilization of a particular class of multi-input linear systems of fractional order differential inclusions with state delay using variable structure control is considered. First, the sliding surface with a fractional order integral formula is defined, and then the sufficient conditions for stability of the sliding surface are derived. Also, the concepts related to sliding control stabilization of differential inclusion systems with integer order are extended to differential inclusion systems with fractional order 0<q<1. Furthermore, for stabilization of fractional order systems with delay in the state space, a feedback and the concept of the norm of a state space is exploited. Finally, simulation results are provided to show the effectiveness of the proposed method.
本文考虑了使用变结构控制对具有状态时滞的特定类多输入线性分数阶微分包含系统的稳定性问题。首先，定义了具有分数阶积分公式的滑动面，然后推导出了滑动面稳定性的充分条件。此外，还将与整数阶微分包含系统滑动控制稳定性相关的概念推广到了 0<q<1 的分数阶微分包含系统中。进一步地，对于状态空间中存在时滞的分数阶系统的稳定性问题，利用了反馈和状态空间范数的概念。最后，提供了仿真结果以验证所提出方法的有效性。
